Commit b4e33143 authored by Florian Rabe's avatar Florian Rabe

no message

parent e01ca943
......@@ -41,12 +41,12 @@ implicit view LeftRegular12LeftRegular : ?LeftRegular1 -> ?LeftRegular =
implicit view Regular2RightRegular1 : ?Regular -> ?RightRegular1 =
include ?Band = ?Band❙
regular = [x,y,z] congT ([u] z∘u) rightregular1
regular = [x,y,z] trans3 assoc5 (congT ([u] z∘u) trans3 assoc4R rightregular1 assoc) assoc4R
implicit view RightRegular12RightRegular : ?RightRegular1 -> ?RightRegular =
include ?Band = ?Band❙
rightregular1 = [x,y,z] congT ([u] x∘u) rightregular
rightregular1 = [x,y,z] trans3 assoc4 (congT ([u] x∘u) trans assocR rightregular) assocR
/T normal bands ❚
......@@ -75,7 +75,7 @@ implicit view Normal2LeftNormal : ?Normal -> ?LeftNormal =
implicit view Normal2RightNormal : ?Normal -> ?RightNormal =
include ?Band = ?Band❙
normal = [x,y,z] congT ([u] z∘u) rightnormal
normal = [x,y,z] trans3 assoc (congT ([u] z∘u) rightnormal) assocR
implicit view LeftNormal2Semilattice : ?LeftNormal -> ?Semilattice =
......
......@@ -32,4 +32,9 @@ theory FOLEQNatDed : http://cds.omdoc.org/urtheories?LF =
congF : {x,y}{F: term ⟶ prop} ⊦ x ≐ y ⟶ ⊦ (F x) ⟶ ⊦ (F y)❘# congF 3 4 5❙
sym : {x,y} ⊦ x ≐ y ⟶ ⊦ y ≐ x❙
trans : {x,y,z} ⊦ x ≐ y ⟶ ⊦ y ≐ z ⟶ ⊦ x ≐ z❙
trans3 : {w,x,y,z} ⊦ w ≐ x ⟶ ⊦ x ≐ y ⟶ ⊦ y ≐ z ⟶ ⊦ w ≐ z❘
= [w,x,y,z,p,q,r] trans (trans p q) r❙
trans4 : {v,w,x,y,z} ⊦ v ≐ w ⟶⊦ w ≐ x ⟶ ⊦ x ≐ y ⟶ ⊦ y ≐ z ⟶ ⊦ v ≐ z❘
= [v,w,x,y,z,p,q,r,s] trans3 (trans p q) r s❙
\ No newline at end of file
......@@ -7,6 +7,16 @@ theory Magma : ?FOLEQNatDed =
theory Semigroup : ?FOLEQNatDed =
include ?Magma❙
assoc: {x,y,z} ⊦ (x∘y)∘z ≐ x∘(y∘z)❙
assocR: {x,y,z} ⊦ x∘(y∘z) ≐ (x∘y)∘z❘
= [x,y,z] sym assoc❙
assoc4: {w,x,y,z} ⊦ ((w∘x)∘y)∘z ≐ w∘(x∘(y∘z))❘
= [w,x,y,z] trans3 (congT ([u]u∘z) assoc) assoc (congT ([u]w∘u) assoc)❙
assoc4R: {w,x,y,z} ⊦ w∘(x∘(y∘z)) ≐ ((w∘x)∘y)∘z❘
= [w,x,y,z] sym assoc4❙
assoc5: {v,w,x,y,z} ⊦ (((v∘w)∘x)∘y)∘z ≐ v∘(w∘(x∘(y∘z)))❘
= [v,w,x,y,z] trans3 (congT ([u]u∘z) assoc4) assoc (congT ([u]v∘u) assoc4)❙
theory Commutative : ?FOLEQNatDed =
......
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